The author has selected material relevant to symmetry and group theory in physics. Entries are marked E (elementary), I (intermediate), and A (advanced) to designate their level. Articles selected for incorporation in a reprint volume (to be published seperately by the American Association of Physics Teachers) are marked with an asterisk().

Past analyses of bow and arrow dynamics have assumed the string to be inextensible. This results in predictions of efficiencies that are significantly higher than measured values (efficiencies over 90% are predicted versus 70% to 85% for measurements, circa 1960). The present analysis allows for an elastic string. It is found that arrow exit then takes place when the string and bow limbs still have substantial kinetic energy, and therefore this energy is unavailable for kinetic energy of the arrow. Moreover, the potential energy remaining in the string and bow limb system can also reduce the amount of energy available for the arrow. For the Hickman model of a long bow used in this study, the elastic string prediction of efficiency is 78%, whereas the inelastic prediction is 92%. The analysis utilizes a Lagrangian distributed mass formulation to develop the governing equations of motion and to generate an equivalent point mass model. The equations of motion were numerically integrated to obtain efficiency, arrow velocity, virtual masses, string tension, string extension, arrow exit time, string and limb potential energies, system momentum, and the dynamic force required to hold the bow handle stationary. Estimates of the effect of air resistance were made and found to be less than 2% of the total system energy. The vibratory dynamics of the string and bow limbs subsequent to arrow exit was analyzed. The results of the elastic string considerations are in reasonable agreement with experimental data and negate the usual explanation for the long‐standing discrepancy between theory and experiment as due to air resistance and hysteresis losses in the string and bow limbs.

In this paper we consider the stability and oscillations (or small motions) of a soap film suspended between parallel coaxial rings. The problem of determining the equilibrium shape of such a film is a standard problem in the calculus of variations, and is often used to introduce variational methods in mechanics texts. However, the stability of the resulting surfaces is usually not discussed, and the small‐motion problem is not analyzed in any standard reference. We show that both the stability and small‐motion problem can be treated quite easily using eigenfunction methods familiar in elementary quantum mechanics. We use these methods to determine the range of parameters for which the solutions to the variational problem (the extremal surfaces) are stable, and analyze the small motions of the film (with examples) near both extremal and nonextremal surfaces.

Based on Weinberg’s work on Lorentz‐transformation properties of massless particles, we discuss the little group for photons and gauge transformations from a pedagogical standpoint. It is pointed out that the ’’translational’’ degrees of freedom associated with the photon little group can generate a transformation which guarantees the transversality of the four‐vector representation for photons. This little‐group transformation, which leaves the photon momemtum invariant, can be regarded as a gauge transformation.

Equilibrium blackbody radiation, like all radiation, is, in general, Doppler shifted if it is emitted and/or reflected from a moving body. The relevance of this fact to the analysis of Maxwell’s demon, which has been previously neglected, is revealed in this paper. In particular, we find that, by appropriately taking advantage of this fact, Maxwell’s demon is, at least in principle, capable of operating, albeit very weakly, in violation of the Second Law of Thermodynamics.

Does a knowledge of physics help to improve one’s basketball skills? Several applications of physical principles to the game of basketball are examined. The kinematics of a basketball shot is studied, and criteria are established for determining the best shooting angle at any given distance from the basket. It is found that there is an optimum shooting angle which requires the smallest launching force and provides the greatest margin for error. Some simple classroom illustrations of Newtonian mechanics based on basketball are also suggested.